Thickness-dependent diffusion coefficient

Section A.2 of the Appendix discusses calculation of the film-thickness-dependent diffusion coefficient from a hydrodynamic model. 

To quantify the spreading characteristics, we examined the thickness-dependent diffusion coefficient D h), extracted from the SME via two methods. The first method utilizes the spreading data at constant height (isoheight), while the second method utilizes the entire... 

To examine the effect of time-dependent diffusion coefficient on the release behavior from a swellable polymer system containing dissolved or dispersed drug, we consider a polymer sheet with half thickness i, an initial drug loading A, a drug solubility in the polymer matrix C, and a time-dependent drug diffusion coefficient of the following form ... 

In dispersive electronic transport, the time dependence of the drift mobility leads to some unusual experimental observations, for example, an apparent thickness and field dependence of the mobility. These same effects enter in the relation between the dispersive hydrogen diffusion and the electronic relaxation time. Following Jackson, Marshall and Moyer (1989), the time-dependent diffusion coefficient is described by... 

Retardation Effects of Polymeric Finishes on Carbonation. The retardation effects of polymeric finishes can be well explained, using equations 9. and 12., where I is the constant term which includes total surface mass transfer constant, and describes the retardation of carbonation or induction period before the carbonation begins to proceed. From equation 9. it can be seen that the effects depend on the thickness and diffusion coefficients of finishes (Figure 13). 

The diffusion coefficient depends upon the characteristics of the absorption process. Reducing the thickness of the surface films increases the coefficient and correspondingly speeds up the absorption rate. Therefore, agitation of the Hquid increases diffusion through the Hquid film and a higher gas velocity past the Hquid surface could cause more rapid diffusion through the gas film. 

Diffusivity and tortuosity affect resistance to diffusion caused by collision with other molecules (bulk diffusion) or by collision with the walls of the pore (Knudsen diffusion). Actual diffusivity in common porous catalysts is intermediate between the two types. Measurements and correlations of diffusivities of both types are Known. Diffusion is expressed per unit cross section and unit thickness of the pellet. Diffusion rate through the pellet then depends on the porosity d and a tortuosity faclor 1 that accounts for increased resistance of crooked and varied-diameter pores. Effective diffusion coefficient is D ff = Empirical porosities range from 0.3 to 0.7, tortuosities from 2 to 7. In the absence of other information, Satterfield Heterogeneous Catalysis in Practice, McGraw-HiU, 1991) recommends taking d = 0.5 and T = 4. In this area, clearly, precision is not a feature. 

A number of metals, such as copper, cobalt and h on, form a number of oxide layers during oxidation in air. Providing that interfacial thermodynamic equilibrium exists at the boundaries between the various oxide layers, the relative thicknesses of the oxides will depend on die relative diffusion coefficients of the mobile species as well as the oxygen potential gradients across each oxide layer. The flux of ions and electrons is given by Einstein s mobility equation for each diffusing species in each layer... 

With regard to the enantioselective transport through the membrane, one advantage of liquid membrane separation is the fact that the diffusion coefficient of a solute in a liquid is orders of magnitude higher as compared to the diffusion coefficient in a solid. The flux through the membrane depends linearly on the diffusion coefficient and concentration of the solute, and inversely on the thickness of the membrane [7]. 

The formation of carbon dioxide depends on both the isocyanate and water concentrations in the paint film. The carbon dioxide concentration in the paint film depends on the diffusion coefficient, the film thickness and the difference in carbon dioxide concentration between paint film and gas phase ... 

An analogy exists between mass transfer (which depends on the diffusion coefficient) and momentum transfer between the sliding hquid layers (which depends on the kinematic viscosity). Calculations show that the ratio of thicknesses of the diffnsion and boundary layer can be written as... 

It is important to note that the dilfnsion-layer thickness depends not only on hydro-dynamic factors but also (through the diffusion coefficient) on the nature of the diffusing species. This dependence is minor, of course, since the values of Dj differ little among the various substances, and in addition are raised to the power one-third in Eq. (4.37). 

The theory has been verified by voltammetric measurements using different hole diameters and by electrochemical simulations [13,15]. The plot of the half-wave potential versus log[(4d/7rr)-I-1] yielded a straight line with a slope of 60 mV (Fig. 3), but the experimental points deviated from the theory for small radii. Equations (3) to (5) show that the half-wave potential depends on the hole radius, the film thickness, the interface position within the hole, and the diffusion coefficient values. When d is rather large or the diffusion coefficient in the organic phase is very low, steady-state diffusion in the organic phase cannot be achieved because of the linear diffusion field within the microcylinder [Fig. 2(c)]. Although no analytical solution has been reported for non-steady-state IT across the microhole, the simulations reported in Ref. 13 showed that the diffusion field is asymmetrical, and concentration profiles are similar to those in micropipettes (see... 

This intercept is referred to as the lag time [4], and it provides a means for estimating the diffusion coefficient provided the membrane thickness is known and with the assumption that other time-dependent processes, such as membrane hydration, do not occur during the lag phase. 

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